Fluid flow calculator



y 1952 J. BARTLETT ETAL.

FLUID FLOW CALCULATOR 2 SHEETSSHEET 1 Filed Aug. 10, 1950 INVENTORS JAMES L. BARTLETT & BY JAMES R. DAV/S m v M ATTORNEYS y 1952. J. L. BARTLETT ETAL 2,597,609

FLUID FLOW CALCULATOR Filed Aug. 10, 1950 2 SHEETSSHEET 2 IIIHHI ATTORNEYS Patented May 20, 1952 TED STATES omci:

/ :Fmmrrz f zemmen -iamesn earuewsna James B Davis Laprosse, Wis, assignors to The "Trane -Company, "La

{This {iiiveirtlon relates rena-an w calculators ahd barticulaf ly to calculators "for determining the factors" of the fiow of fluids in "conduits and more particularly for' determihing the nature of the flow 'of'airin ducts.

{It *is"-an -*obiect =of this invention to {provide a s'li'derule calculator vvhich is ihiip'e'nsivc "to construct arid whicjlr is-accurate and easyto use.

It is aribb'ject of thisihVhtibn to "provide a mechahicalfrule mde'ter miningthe round duct s'izef rectangular duct 'size, the a ir volume, the air Iriction,'-' and; the 1 air veiocity by a single setting offt-he'sl ide rule to any "two of 'the above'factors one-'oftvhi'ch must beeitherthe duct size orthe airvolume.

It is another-objector this-invention tobrovide a mechariicalrule "for determiningrectan'gular-ducts of various major andminor axes which are-eqiiiva1enttoa givenround*duct and vice versa.

'-'It-is "another *dbjct of this 'ir'ivention' 'to' provide "a stop memberfor liniiting adjustment of the device tothe *efiectiverange ofmovement.

--()th'er obj ects and advantages win "appear as the-specification"proceeds to describe' 'theinvention with referenceto the accompanyin drawings,-inwl'iich Fig: I is' a iilan'view'of the lide rule calculator of this in'vrflaion.

m 2" 15 a 'cross-sectionaiviewtakenbn :the line 2- 2 of fFig. 1. g V

Fig? 3 1s a view of-"the 'base member of the slide rulecalculator. v v i I "Referrin g now to Fig. "1} a base member 1 0 has an 'indek'alb le member 12 rdtatabi ysecu'rea thereon by a rivet l 4 which extends through *the members and I2 neartheir geometric centers. Base member fo hasa -hdle l3 for receiving rivet l4.

Indexable member J2 has an arcuate slot l6 therein having its arcuate center on the pivotal axis ofindxable member l2. The s1ot'l6-need not be arcuate in shape, because it functionsiiierely to permit observation-of abortion ofbase-member I 0. An arcuate logarithmic scale 8 .of round ductdiamete'rs in inches is printed 'onfthe basemember Won afradius' from'the pivotal axis such thatth'e scale 18 appears through the a'rcuzite'slot IS in indexable member I 2, An indicating arrow 2015 printed 'o n member l2 at or near-"the icepterbr ene edge of the arcuate'slot" [6. It is preferred to locate the arrow on the 'mne'r'e'age of the 'arcnare slot I6. An arcuate logarithmic scale 22 of duct friction in inches of water per 100 feet of duct is printed on the periphery of indexable member I 7 'An a qa saie "so offrectaiigiilariduct dimansions in'l'r icli'esfis printe theberibhry of indeizable memberu. The arcuatelscale 30' has a center which is's'baced from the pivotal axis of member l2. The scale 30, .the'refore,sweeps ever the me or member to. 'A s cale 32' of freetangular duct dimensions 115 printe ion base member [0. Scale 32 has lorig"divisionliiiesjto register with the scale 30 throughout its range of pivotal movement. I

Base member l0 hasan arcu ate slot 34. A rivet 36 is fastened to member and extends into the s t lin me b r 10- fljhey f efiifi a te a he 8 o P v d agemen o t r ire f o memb r D-v, h n r me t 9i. h r t-3'6 imi ed, -t im 4 and eoe en h i o me e e fi i t li exa l m ii ber I? with spect 9 the base mem er in s elsef mi ee.

eqes lf eeiin the saltwater t foilbwin'e symbols are used in the calculations:

F- Friction in inches or "water -per ft. or

"ductflehgth. I v I I Q Quant'ity in cubic feetberfminute.

til-Diameter of round duct "in inches.

. (I -Rectangular duct" dimension in {inches Ii -Rectangular ductdimension in i'nch'es.

miem ggiiifintatisn "me rbiiwi'ng reiafiidnship fisi'found to exist. H (l) WV 11"". 11000 The formula for' flow inaduct is' given' beloivz (2) 1rd V --(-4)( 144') Q Cbn b sham 1. da l l hfdi k' iie th logarithm of both sides of the combined equations,

(3) log (1:.378 log Q-.199 log F.l93

3 Taking the logarithm of both sides of Equation 2 results in Equation 4.

(4) Log d= log Q log V+% log 183 A logarithmic scale 18 for d is laid out on the base member and the indicating arrow is marked on the indexable member I2. Scales 280/) and 28(Q) are then constructed. From Equation 4 it is found that the angle subtended by a logarithmic cycle on scales (V) and 28(Q) must be one half the angle subtended by a logarithmic cycle on scale [8(d) because the coeflicients of log Q and log V are both of the coefficient of log d in Equation 4.

Scales 22 and 24 are now constructed. From Equation 3 it is found from the coefiicients of the terms, that the angle subtended by a cycle on scale 22(F) must be .199 times the angle subtended by a cycle on scale l8(d) and the angle subtended by a logarithmic cycle on scale 24(Q) must be .378 times the angle subtended by a logarithmic cycle on scale [8(d). The scales 22 and 24 may be constructed on a different radius than that of scale l8(d) provided that the angles subtended by the logarithmic cycles of the scales bear the relationship required by the coefficients of the terms of Equation 3. It should also be understood that scale 22 could be on member I0 and scale 24 on member l2 if desired. Scales 2G and 28 could also be interchanged between members [9 and 12 if desired.

In determining the angular position of scale 22 with respect to the indicating arrow 20 for a given angular position of the scale 24, it is only necessary to adjust the member :2 so that the indicating arrow 20 is opposite a value for d on scale [8 and to then angularly position the scale 22 on member i2 so that Equation 3 is satisfied. The angular location of scale 26 on indexable member [2 is determined in like manner using Equation 4.

The scales 30 and 32 are determined by the following formula:

Scale 38 is arbitrarily laid out on the arc of a circle having a center spaced from the axis of rotation of indexable member l2. The locations of points on the division lines of scale 32 are then calculated for various values of (d) until the division lines of scale 32 can be plotted.

It is evident from the above description that the calculator of this invention determines the round duct size, the rectangular duct size, the air volume, the air friction, and the air velocity by a single setting of the indexable member to any two of the above factors one of which must be either the duct size or the air volume.

The calculator may be used for calculating rectangular ducts which are equivalent to a given diameter of circular duct and vice versa.

While we have described the foregoing preferred embodiments of our invention, we contemplate that many changes may be made without departing from the scope and spirit of our invention and we desire to be limited only by the claims.

We claim:

1. A fluid flow calculator comprising a base member, an indexable member, means pivotally mounting said indexable member on said base member, a first fluid volume scale on one of said members, a fluid friction scale on the other of said members from that having said first fluid volume scale, said fluid friction scale registering with said first fluid volume scale, a second fluid volume scale on one of said members, a fluid velocity scale on the other of said members from that having said second fluid volume scale, said fluid velocity scale registering with said second fluid volume scale, a first scale of rectangular duct dimensions on one of said members, the division lines of said first scale of rectangular duct dimensions being curved, a second scale of rectangular duct dimensions on a portion of the periphery of the other of said members from that having said first scale of rectangular duct dimensions, said portion of the periphery oi the other of said members having throughout its length progressively increasing radii with respect to said pivotally mounting means, a scale of circular duct dimensions on one of said members and indicating means on the other of said memhere from that having said scale of circular ducts dimensions, said indicating means registering with said scale of circular duct dimensions, each of said scales being proportioned and being positioned with respect to each other and with respect to said indicating means according to a mathematical relationship for fluid flow.

2. A fluid flow calculator comprising a base member, an indexable member, means pivotally mounting said indexable member on said base member, a first fluid volume scale on one of said members and a fluid friction scale on the other of said members registering with said first fluid volume scale, a second fiuid volume scale on one of said members and a fluid velocity scale on the other of said members registering with said second fluid volume scale, a scale of circular duct dimensions on one of said members and indicating means on the other of said members registering with said scale of circular duct dimensions, a first scale of rectangular duct dimensions on said base member, the division lines of said first scale of rectangular duct dimensions being curved, a portion of the periphery of said indexable member conforming substantially to an arc of a circle offset from the pivotal axis of said indexable member, a second scale of rectangular duct dimensions on said portion of the periphery of said indexable member and registering with said first scale of rectangular duct dimensions, said indicating means and each of said scales being positioned and proportioned with respect to each other according to a mathematical relationship for fluid flow.

JAMES L. BARTLETT. JAMES R. DAVIS.

Name Date McDowell Jan. 29, 1946 OTHER REFERENCES Special Slide Rules, by J. N. Arnold, pages 18-19; published by Purdue University, La Fayette, Indiana, September 1933.

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